I agree that first of all you must talk to them and tell that you've noticed that they lie when it comes to actual hours worked. Tell that you're going to check this more throughly and if they keep lying, you'll have to punish them. I think that this will help))
And if there are any insolent employees who keep leaving work earlier, you can start trackimg them with an employee monitoring program, video camera or time trackers. Let them know that they are monitored and they will stop sirupting the schedule...
I think that it's normal to track lazy people... Being a Big Brother is sometimes a must.
Hey there! My company uses video surveillance cameras, plus they installed an employee monitoring application on every device which tracks every user activity, even keystrokes and chats)) luckily, our boss has warned us of this app so I simply don't use my social networks on the company computer)) so in fact, a company can track any activity, not only browsing history...